Artificial Intelligence II

Transcription

1 Artificial Intelligence II 2013/ Prof: Daniele Nardi, Joachim Hertzberg Exercitation 3 - Roberto Capobianco Planning: STRIPS, Partial Order Plans, Planning Graphs 1

2 STRIPS (Recap-1) Start situation; Goal conditions; Operator schemata Preconditions; Postconditions; Plan: pair O, < of a set O of operator instances and an ordering relation < on O. Operator: pair R, S of sets R, S of ground facts. R: operator s preconditions (what must be true to execute it?); S: postconditions (what are the effects of its execution?); Progression or Regression: Progression: search forward from initial state to goal; Regression: search backward from goal to initial state. 2

3 STRIPS (Recap-2) STRIPS Algorithm, with Regression: 3

4 STRIPS & Shakey Stanford Robot controlled by STRIPS; At the time planner could find plans beyond robots abilities; Actions: Move; Pushing movable objects; Climb onto and down from objects; Turn light switches on and off. 4

5 Shakey Problem (1) Describe Shakey s Actions in STRIPS: Go(x, y) where x and y are locations in the same room (there is a door between the rooms); Push(b, x, y) to push box b from x to y (both locations in the same room); ClimbUp(b, x) and ClimbDown(b, x) TurnOn(s, x) and TurnOff(s, x); 5

6 Shakey Problem (2) Describe: The initial state in figure; The goal state where Box2 is in Shakey s initial position; Construct a plan using Progression and one using Regression. 6

7 Shakey s Actions (1) Action( GoTo(x, y), PRECOND : At(Shakey, x) x y sameroom(x, y) EFFECT : At(Shakey, x) At(Shakey, y) ) Action( Push(b, x, y), PRECOND : Box(b) At(b, x) x y sameroom(x, y) At(Shakey, x) EFFECT : At(b, x) At(b, y)) At(Shakey, x) At(Shakey, y) ) 7

8 Shakey s Actions (2) Action( ClimbUp(b, x), PRECOND : Box(b) At(Shakey, x) At(b, x) OnABox EFFECT : On(b) OnABox ) Action( ClimbDown(b, x), PRECOND : Box(b) At(Shakey, x) At(b, x) On(b) OnABox EFFECT : On(b) OnABox ) 8

9 Shakey s Actions (3) Action( TurnOn(s, x), PRECOND : SwitchOff(s) Switch(s) At(Shakey, x) At(s, x) OnABox EFFECT : SwitchOff(s) ) Action( TurnOff(s, x), PRECOND : SwitchOff(s) Switch(s) At(Shakey, x) At(s, x) OnABox EFFECT : SwitchOff(s) ) 9

10 Shakey s Initial State Boxes: Box(B1) Box(B2) Positions: At(Shakey, I) At(B1, PB1) At(B2, PB2) At(S1, PS1) At(S2, PS2) Switches: Switch(s1) Switch(s2) SwitchOn(s2) SwitchOff(s1) Doors: sameroom(pb1, PB2) sameroom(pb2, PB1) sameroom(pb1, PS2) sameroom(ps2, PB1) sameroom(pb2, PS2) sameroom(ps2, PB2) sameroom(i, PS1) sameroom(ps1, I) Goal: At(B2, I) 10

11 Shakey s Solution There is no plan! (No door between the rooms). 11

12 PDDL PDDL (Planning Domain Definition Language); Definition of: Predicates; Actions/Operators; Objects; Initial state; Goal; Planning tasks specified in PDDL are separated into: A domain file for predicates and actions; A problem file for objects, initial state and goal specification. 12

13 PDDL Files Domain file: (define (domain <domain name>) <PDDL code for predicates> <PDDL code for first action> [...] <PDDL code for last action> ) Problem file: (define (problem <problem name>) (:domain <domain name>) <PDDL code for objects> <PDDL code for initial state> <PDDL code for goal specification> ) 13

14 Shakey Problem in PDDL (1) Predicates: (:predicates (at?x?y) (on?x?y) (in?x?y) (box?x) (turnedon?x)) Actions: (:action Go :parameters (?x?y?r) :precondition (and (on Shakey Floor) (at Shakey?x) (in?x?r) (in?y?r)) :effect (and (at Shakey?y) (not (at Shakey?x)))) (:action Push :parameters (?b?x?y?r) :precondition (and (on Shakey Floor) (at Shakey?x) (box?b) (at?b?x) (in?x?r) (in?y?r)) :effect (and (at Shakey?y) (at?b?y) (not (at Shakey?x)) (not (at?b?x)))) 14

15 Shakey Problem in PDDL (2) (:action ClimbUp :parameters (?x?b) :precondition (and (on Shakey Floor) (at Shakey?x) (at?b?x) (box?b)) :effect (and (on Shakey?b) (not (on Shakey Floor)))) (:action ClimbDown :parameters (?b) :precondition (and (on Shakey?b) (box?b)) :effect (and (on Shakey Floor) (not (on Shakey?b)))) (:action TurnOn :parameters (?s?b) :precondition (and (on Shakey?b) (box?b) (at?b?s)) :effect (turnedon?s)) 15

16 Shakey Problem in PDDL (3) (:action TurnOff :parameters (?s?b) :precondition (and (on Shakey?b) (box?b) (at?b?s)) :effect (not (turnedon?s))) Objects: (:objects Shakey Floor START Room1 Room2 Door1 Door2 Switch1 Switch2 Box1 Box2 BX1 BX2) 16

17 Shakey Problem in PDDL (4) Initial state: (init: (on Shakey Floor) (at Shakey START) (in START Room1) (box Box1) (at Box1 BX1) (in BX1 Room2) (box Box2) (at Box2 BX2) (in BX2 Room2) (in Door1 Room1) (in Switch1 Room1) (not (turnedon Switch1)) (in Door2 Room2) (in Switch2 Room2) (turnedon Switch2) Goal: (:goal (and ( ) ( )) Get your plan (e.g., use blackbox: 17

18 PDDL Exercise (in Class) Gripper task with four balls: There is a robot that can move between two rooms and pick up or drop balls with either of his two arms. Initially, all balls and the robot are in the first room. We want the balls to be in the second room. Objects: 2 rooms, 4 balls and 2 robot arms. Predicates: room(x), ball(x), at-ball(b, r), free(x), etc.; Initial state: all balls and the robot are in the first room, all robot arms are empty, etc.; Goal specification: all balls must be in the second room. Actions/Operators: the robot can move between rooms, pick up a ball or drop a ball. 18

19 STRIPS Exercise (in Class - 1) An explorer robot must go on a journey with a jeep. To be able to travel he must: refill the jeep s tank and an fill extra tank to put in the car trunk; put in his backpack a bottle of wine and a sandwich; put the prepared backpack, the binoculars and a map in the jeep. Before filling the bottle he must clean it. Suppose that in the initial state the robot is close to the jeep, and all the object and goods required are close to the jeep. The goal state is to have the robot ready to travel. 19

20 STRIPS Exercise (in Class 2) Using STRIPS: Describe the initial state. Describe the goal state. Describe the actions. 20

21 Partially Ordered Plans (Recap) How to practically get POPs: 1. Initial plan, containing two steps called «start» and «finish»: «start» has the initial conditions as its effects; «finish» has the goal conditions as its preconditions; 2. Iterate until the plan is complete (i.e., every precondition at each step is satisfied by the effect of some other step): a. Choose a subgoal (i.e., a precondition p not yet satisfied); b. Choose an operator that can satisfy p; c. Check that the work done in the previous step doesn t violate any of our previous causal links: if it happens, resolve the threat. 21

22 POPs: Choose (Recap) We want p to be true: Find some step already in the existing plan, having p as an effect OR add a new step to the plan; Choose: arbitrary choose for execution one operator within a set of possible things that could be done; Fail: if you fail (i.e., there is no operator that makes p true) just go back to the most recent choice and try a different option; If they have all been tried: go recursively (i.e., go back to the most recent choice); If you fail up to the top level of the program, there is no plan. 22

23 POPs: Causal Links (Recap) If you find an operator that can make p true: Choose that step from the already available plan or add a new step to the plan by instantiating that operator; Add a causal link between the two steps; Add an ordering constraint between the two steps (the new step goes before the one requiring p); If needed: Add a variable binding constraint (e.g., for binding a variable in the new step with p); If the new constraint is incompatible with the existing constraints, fail (i.e., go back to ). 23

24 POPs: Resolve Threats (Recap) A step s could violate a causal link by undoing the «work» previously done to estabilish a certain value of p, making it impossible to execute successive operators; How to deal with threats: Promotion: move s in such a way that it comes before the operator establishing the value of p; Demotion: move s in such a way that it comes after the value of p is used for the execution of successive operators; If promotion fails, try demotion; If both fail, try a different way to satisfy p; If variables appear in the operator, try to constraint the variables in such a way that it has not negative effects in s; 24

25 POP Example (1) Define the ordering constraints and the causal links among the actions, and produce a partially ordered plan to solve the problem. 25

26 POP Example (2) 26

27 POP Example (3) 27

28 POP Example (3) NOTE: PutOn(A,B) clobbers Cl(B): order after PutOn(B,C) 28

29 POP Example (4) NOTE: PutOn(B,C) clobbers Cl(C): order after PutOnTable(C) 29

30 POP Example (5) 30

31 POP Exercise (in Class) Produce the POP for the following problem: Action Buy(x, store) Go(x, y) PRECOND: At(store), Sells(store, x) EFFECT: Have(x) PRECOND: At(x) EFFECT: At(y), At(x) Goal Have(Milk) Have(Banana) Have(Drill) 31

32 Planning Graphs (Recap - 1) Two (different!) operators in a layer are exclusive: in layer O 0 iff they interfere; in layer O i >0 iff they interfere or compete; Two operators interfere iff one destroys a precondition or an effect of the other; Two operators compete in layer O i, iff they have facts among their preconditions that are exclusive on the previous layer F i ; Two facts f, g are exclusive in layer F i >0 iff there are only exclusive operators in the previous layer O i 1 that produce f and g. 32

33 Planning Graphs (Recap 2) Generate solving planning graph; Extract mutex-free plan; If no mutex-free plan found, extend planning graph; Expansion of a planning graph G n = N,E of the order n: add operator layer O n, fact layer F n+1, and mutex arcs; An expansion fixed point is a planning graph, in which two fact layers and all their mutex conditions are identical. 33

34 Planning Graphs (Recap 3) 34

35 Planning Graphs Example (1) Initial state: garbage cleanhands quiet Goal state: dinner present garbage Actions: Cook: PRECOND: cleanhands; EFFECT: dinner Wrap: PRECOND: quiet; EFFECT: present Carry: EFFECT: garbage cleanhands Dolly: EFFECT: garbage quiet 35

36 Planning Graphs Example (2) wrap and dolly are mutex because dolly negates the precondition of wrap; carry and the no-op are mutex because one negates the effect of the other; present and quiet are mutex because the actions achieving them, wrap and dolly, are mutex. 36

37 Planning Graphs Example (3) 37

38 Thank you! 38